Q. 3 Sketching parametric equations: ... [FREE SOLUTION]

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Chapter 9: Q. 3 (page 774)

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos t$ , $t 鈭� [0, 4 蟺]$ .

Short Answer

Expert verified

The graph is circle in clockwise.

Step by step solution

Step 1. Given Information.

The equations are $x = \sin t$ and $y = \cos t$ such that $t 鈭� [0, 4 蟺]$ .

Step 2. Explanation.

Start by eliminating the parameter. Square the equations for x and y,

So,

$x^{2} = \sin^{2} t$

$y^{2} = \cos^{2} t$

Apply the Pythagorean identity.

$\sin^{2} t + \cos^{2} t = 1$

So, $x^{2} + y^{2} = 1$

So, this is a circle of radius 1 and centered at the origin.

Step 3. Calculation

To know the direction make a table as follows,

t	0	$蟺$	$2 蟺$	$4 蟺$
$x = \sin t$	$\sin 0 = 0$	$蝉颈苍蟺 = 0$	$\sin 2 蟺 = 0$	$\sin 4 蟺 = 0$
$y = \cos t$	$\cos 0 = 1$	$肠辞蝉蟺 = - 1$	$\cos 2 蟺 = 1$	$\cos 4 蟺 = 1$

Draw the graph as follows,

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91影视

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos t$ , $t 鈭� [0, 4 蟺]$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation

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91影视

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.x=sint,y=cost,t鈭�0,4蟺.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Logic and Functions

Applied Mathematics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos t$ , $t 鈭� [0, 4 蟺]$ .